// Magma code for the lmfdb family of higher genus curves 9.57-1.0.3-3-19.1
// The results are stored in a list of records called 'data'

RecFormat:=recformat<group,gp_id, signature,gen_vectors,conj_classes,genus,dimension,r,g0, passport_label,gen_vect_label, is_hyperelliptic, hyp_involution, is_cyclic_trigonal,cyc_auto,full_auto, full_sign,topological_class,braid_class>;

data:=[];

// Create group as a permutation group, and generate data which is the same for all entries.
gp_id:=[57,1];
H:=SmallGroup(gp_id[1],gp_id[2]); n:=#H; LP:=[]; LG:=[g : g in H]; for i in [1..n] do x:=LG[i]; Tx:=[LG[j]*x : j in [1..n]]; permL:=[]; for j in [1..n] do for k in [1..n] do if Tx[j] eq LG[k] then permL[j]:=k;  break; end if; end for; end for; Append(~LP,permL); end for; G:=PermutationGroup<n|LP>; 
signature:=[0,3,3,19];
genus:=9;
r:=#signature-1;
g0:=signature[1];
dim:=3*g0-3+r;
S:=Sym(gp_id[1]);

// Here we add an action to data.
gen_vectors:=[[20, 27, 34, 22, 29, 36, 24, 31, 38, 26, 33, 21, 28, 35, 23, 30, 37, 25, 32, 39, 46, 53, 41, 48, 55, 43, 50, 57, 45, 52, 40, 47, 54, 42, 49, 56, 44, 51, 1, 8, 15, 3, 10, 17, 5, 12, 19, 7, 14, 2, 9, 16, 4, 11, 18, 6, 13], [57, 49, 41, 52, 44, 55, 47, 39, 50, 42, 53, 45, 56, 48, 40, 51, 43, 54, 46, 19, 11, 3, 14, 6, 17, 9, 1, 12, 4, 15, 7, 18, 10, 2, 13, 5, 16, 8, 38, 30, 22, 33, 25, 36, 28, 20, 31, 23, 34, 26, 37, 29, 21, 32, 24, 35, 27], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 20, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 39]];
cc:=[2,3,4];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);
